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from matplotlib import pyplot;
from pylab import genfromtxt;  
import matplotlib.pyplot as plt
import numpy as np
from mpl_toolkits.mplot3d import Axes3D
########### FITTED GAUSSIAN (red) ##############
# Load file into mat0
mat0 = genfromtxt("0005.map");

#PLOT FIGURE 
fig = plt.figure(figsize=(20,10))
ax = plt.axes(projection='3d')

#Define Gaussian function
def twoD_Gauss((x,y),amplitude,x0,y0,sigma_x,sigma_y,offset):
    x0=float(x0)
    y0=float(y0)
    return offset + amplitude*np.exp(-(((x-x0)**(2)/(2*sigma_x**(2))) + ((y-y0)**(2)/(2*sigma_y**(2)))))

# Create x and y indices
x = mat0[:,0]
y = mat0[:,1]

#create data
data = mat0[:,2]

#plt.imshow(data)
import scipy.optimize as opt
initial_guess = (24000,150,143,25,25,6000)

#Fit Gaussian function
params, pcov = opt.curve_fit(twoD_Gauss, (x,y), data,initial_guess)

#Print fitted parameters
print(params)

#Plot fitted Gaussian
ax.plot_trisurf(x-150, y-143, twoD_Gauss((x,y),*params), cmap="Reds", linewidth=0,alpha=0.5)
ax.set_xlabel('x / mm')
ax.set_ylabel('y / mm')

#Plot settings
ax.view_init(0, 270)

########### SIMULATED GAUSSIAN (blue) ##############
#functions  
w0=1.701
lamb=0.90846
d_in1=45.0
foc1=38.35
zR=np.pi*w0**(2)/(lamb)
w1=w0*np.sqrt(1/(((d_in1)/foc1-1)**(2)+(zR/foc1)**(2)))    
zR1=np.pi*w1**(2)/(lamb)
foc2=420
d_in2=499.8971
d_2=606
d_out2=foc2+(d_in2-foc2)/(((d_in2)/foc2-1)**(2)+(zR1/foc2)**(2))
w2=w1*np.sqrt(1/(((d_in2)/foc2-1)**(2)+(zR1/foc2)**(2)))
zR2=np.pi*w2**(2)/(lamb)

u=w2*np.sqrt(1+((3001-d_in1-d_2-d_out2)/zR2)**(2))

def i_3(x,y):
    return 3818017.483*(w0/u)**(2)*np.exp(-(2*(x**(2)+y**(2)))/(u**(2)))+7115.230

#define x and y
x = np.linspace(-50, 50, 100)
y = np.linspace(-50, 50, 100)
X, Y = np.meshgrid(x,y)
Z = i_3(X,Y)

#Plot settings
ax.xaxis.set_pane_color((1.0, 1.0, 1.0, 0.0))
ax.yaxis.set_pane_color((1.0, 1.0, 1.0, 0.0))
ax.zaxis.set_pane_color((1.0, 1.0, 1.0, 0.0))
ax.xaxis._axinfo["grid"]['color'] =  (1,1,1,0)
ax.yaxis._axinfo["grid"]['color'] =  (1,1,1,0)
ax.zaxis._axinfo["grid"]['color'] =  (1,1,1,0)
ax.w_zaxis.line.set_lw(0.)
ax.set_zticks([])
ax.view_init(-1, 215)

#Plot
surf=ax.plot_surface(X,Y,Z,rstride=1,cstride=1,cmap='Blues', edgecolor='none', alpha=1.0)

#print(I)
ax.text(10,100,12000,'Fitted Gaussian',color='red',fontsize=18)
ax.text(10,100,14000,'Simulated Gaussian',color='blue',fontsize=18)
plt.show()

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∫_{-∞}^{∞} ϕ(x, μ, σ) dx = 1.

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A = ∫_{-∞}^{∞} (f(x) - g(x)) dx 
= ∫_{-∞}^{∞} (α ϕ(x, μ_1, σ_1) - β ϕ(x, μ_2, σ_2)) dx
= α - β